Simplifying maximum flow computations: The effect of shrinking and good initial flows
Liers F, Pardella GL (2011)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2011
Journal
Publisher: Elsevier
Book Volume: 159
Pages Range: 2187-2203
Journal Issue: 17
DOI: 10.1016/j.dam.2011.06.030
Abstract
Maximum flow problems occur in a wide range of applications. Although already well studied, they are still an area of active research. The fastest available implementations for determining maximum flows in graphs are either based on augmenting path or on pushrelabel algorithms. In this work, we present two ingredients that, appropriately used, can considerably speed up these methods. On the theoretical side, we present flow-conserving conditions under which subgraphs can be contracted to a single vertex. These rules are in the same spirit as presented by Padberg and Rinaldi (1990) [12] for the minimum cut problem in graphs. These rules allow the reduction of known worst-case instances for different maximum flow algorithms to equivalent trivial instances. On the practical side, we propose a two-step max-flow algorithm for solving the problem on instances coming from physics and computer vision. In the two-step algorithm, flow is first sent along augmenting paths of restricted lengths only. Starting from this flow, the problem is then solved to optimality using some known max-flow methods. By extensive experiments on instances coming from applications in theoretical physics and computer vision, we show that a suitable combination of the proposed techniques speeds up traditionally used methods. © 2011 Elsevier B.V. All rights reserved.
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Germany (DE)How to cite
APA:
Liers, F., & Pardella, G.L. (2011). Simplifying maximum flow computations: The effect of shrinking and good initial flows. Discrete Applied Mathematics, 159(17), 2187-2203. https://dx.doi.org/10.1016/j.dam.2011.06.030
MLA:
Liers, Frauke, and Gregor L. Pardella. "Simplifying maximum flow computations: The effect of shrinking and good initial flows." Discrete Applied Mathematics 159.17 (2011): 2187-2203.
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